Forced induction.
This is a subject that was vigorously & robustly debated in an extensive thread not so long ago, so have a play with the search function & you will likely find it.

Myself, & a few others prefered the ability of the positive displacement blower to deliver high levels of torque, almost instantly, at very low engine speeds, while a large number of others prefered the advantages that a turbo offers at higher engine speeds.
The turbo debate was further broken down into blow through versus suck through.

See if you can find this thread & have a read through it all. With some luck you will gain an insight of the advantaged & disadvantages offered by each system.